{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b760a0f6",
   "metadata": {},
   "source": [
    "# Linear Regression\n",
    "\n",
    "In this notebook, we show how to create, train and evaluate a linear regression model using Concrete ML library, our open-source privacy-preserving machine learning framework based on fully homomorphic encryption (FHE). \n",
    "\n",
    "First, we generate a random clear data-set. Then, we compare 2 linear regression models :\n",
    "\n",
    "- `sklearn_lr` : from Sklearn, which is trained, tested and evaluated on clear data.   \n",
    "- `concrete_lr` : from Concrete ML, which is trained on clear data. Then, quantized and compiled it in FHE. Finally, we test it on _encrypted data_.\n",
    "\n",
    "This notebook aims to show how easy it is to use Concrete ML and how FHE allows to secure the data during the inference phase.\n",
    "\n",
    "Let's get started."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4466e77",
   "metadata": {},
   "source": [
    "### Import libraries\n",
    "\n",
    "We import the required packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6200ab62",
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "\n",
    "import numpy as np\n",
    "from sklearn.datasets import make_regression\n",
    "from sklearn.linear_model import LinearRegression as SklearnLinearRegression\n",
    "from sklearn.metrics import r2_score\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "from concrete.ml.sklearn import LinearRegression as ConcreteLinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f43e2387",
   "metadata": {},
   "source": [
    "And some helpers for visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d104c8df",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display\n",
    "\n",
    "train_plot_config = {\"c\": \"black\", \"marker\": \"D\", \"s\": 15, \"label\": \"Train data\"}\n",
    "test_plot_config = {\"c\": \"red\", \"marker\": \"x\", \"s\": 15, \"label\": \"Test data\"}\n",
    "\n",
    "\n",
    "def get_sklearn_plot_config(r2_score=None):\n",
    "    label = \"Scikit-Learn\"\n",
    "    if r2_score is not None:\n",
    "        label += f\", {'$R^2$'}={r2_score:.4f}\"\n",
    "    return {\"c\": \"blue\", \"linewidth\": 2.5, \"label\": label}\n",
    "\n",
    "\n",
    "def get_concrete_plot_config(r2_score=None):\n",
    "    label = \"Concrete ML\"\n",
    "    if r2_score is not None:\n",
    "        label += f\", {'$R^2$'}={r2_score:.4f}\"\n",
    "    return {\"c\": \"orange\", \"linewidth\": 2.5, \"label\": label}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53e676b8",
   "metadata": {},
   "source": [
    "### Generate a data-set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "410b90de",
   "metadata": {},
   "outputs": [],
   "source": [
    "# pylint: disable=unbalanced-tuple-unpacking\n",
    "X, y = make_regression(\n",
    "    n_samples=200, n_features=1, n_targets=1, bias=5.0, noise=30.0, random_state=42\n",
    ")\n",
    "# pylint: enable=unbalanced-tuple-unpacking\n",
    "\n",
    "# We split the data-set into a training and a testing set\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=42)\n",
    "\n",
    "# We sort the test set for a better visualization\n",
    "sorted_indexes = np.argsort(np.squeeze(X_test))\n",
    "X_test = X_test[sorted_indexes, :]\n",
    "y_test = y_test[sorted_indexes]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a37dc42",
   "metadata": {},
   "source": [
    "We display the data-set to visualize the data distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9618f910",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.ioff()\n",
    "\n",
    "plt.clf()\n",
    "fig, ax = plt.subplots(1, figsize=(10, 5))\n",
    "fig.patch.set_facecolor(\"white\")\n",
    "ax.scatter(X_train, y_train, **train_plot_config)\n",
    "ax.scatter(X_test, y_test, **test_plot_config)\n",
    "ax.legend()\n",
    "display(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75f4fdb7",
   "metadata": {},
   "source": [
    "### 1. LinearRegression model from Sklearn \n",
    "\n",
    "We train the scikit-learn LinearRegression model on clear data and then we test it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2a124a62",
   "metadata": {},
   "outputs": [],
   "source": [
    "sklearn_lr = SklearnLinearRegression()\n",
    "sklearn_lr.fit(X_train, y_train)\n",
    "y_pred = sklearn_lr.predict(X_test)\n",
    "\n",
    "# Compute the R2 scores\n",
    "sklearn_r2_score = r2_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0ba5509",
   "metadata": {},
   "source": [
    "We can visualize our predictions to see how the scikit-learn model performs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "edcd361b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.ioff()\n",
    "plt.clf()\n",
    "\n",
    "fig, ax = plt.subplots(1, figsize=(10, 5))\n",
    "fig.patch.set_facecolor(\"white\")\n",
    "ax.scatter(X_train, y_train, **train_plot_config)\n",
    "ax.scatter(X_test, y_test, **test_plot_config)\n",
    "ax.plot(X_test, y_pred, **get_sklearn_plot_config(sklearn_r2_score))\n",
    "ax.legend()\n",
    "display(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "996fbe05",
   "metadata": {},
   "source": [
    "### Prerequisites\n",
    "\n",
    "Some prerequisites should be reviewed before deep diving !\n",
    "\n",
    "Quantization is a technique that converts continuous data (floating point, e.g., in 32-bits) to discrete numbers\n",
    "within a fixed range (e.g., integer in 8-bits). This means that some information is lost during the process. However, the larger is the integers' range, the smaller the error becomes, making it acceptable to some cases.\n",
    "\n",
    "To learn more about quantization, please refer to this [documentation section](../explanations/quantization.md).\n",
    "\n",
    "Regarding FHE, the input data type must be represented exclusively as integers, making the use of quantization necessary. Therefore, a linear model trained on floats is quantized into an equivalent integer model using _Post-Training Quantization_. This operation can lead to a loss of accuracy compared to the standard floating point models working on clear data. \n",
    "\n",
    "In practice however, this loss is usually very limited with linear FHE models as they can consider very large integers, with up to 50 bits in some cases. This means these models can quantize their inputs and weights over large number of bits (e.g., 16) while still considering data-sets containing many features (e.g., 1000). We therefore often observe almost identical performance scores (e.g., R2 score) between float, quantized and FHE models.  \n",
    "\n",
    "To learn more about the relation between the maximum bit-width reached within a model, the bits of quantization used and the data-set's number of features,  please refer to this [documentation section](../explanations/pruning.md#pruning-in-practice)."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "60cddf91",
   "metadata": {},
   "source": [
    "### 2. Linear Regression model with Concrete ML\n",
    "\n",
    "The typical development flow of a Concrete ML model is the following:\n",
    "\n",
    "- The model is trained on clear (plaintext) data as only FHE inference is currently supported\n",
    "\n",
    "- The resulting trained model is quantized using a `n_bits` parameter set by the user, which can either be:\n",
    "\n",
    "    1. a dictionary composed of `op_inputs` and `op_weights` keys. These parameters are given as \n",
    "    integers representing the number of bits over which the associated data should be quantized.\n",
    "\n",
    "    2. an integer, representing the number of bits over which each input and weight should be quantized.\n",
    "    Default is 8.\n",
    "\n",
    "- The quantized model is compiled to an FHE equivalent following 3 steps:\n",
    "\n",
    "    + create an executable operation graph\n",
    "\n",
    "    + check that the op-graph is FHE compatible by checking the maximum bit-width needed to execute the model\n",
    "\n",
    "    + determine cryptographic parameters that will help to generate the secret keys and evaluation keys. \n",
    "    If no parameters can be found, the compilation process can't be completed and an error is thrown. \n",
    "    The user then can either lower the value(s) chosen for `n_bits` or decrease the number of features \n",
    "    found in the data-set (using techniques such as [PCA](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html))\n",
    "    and run the development flow once again.\n",
    "\n",
    "- Inference can then be done on encrypted data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4f2f6d8",
   "metadata": {},
   "source": [
    "### 2.1 Quantized Linear Regression without FHE\n",
    "\n",
    "In this example, we show you how to quantize a model with Concrete ML, and how to train and test it on plaintext data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "06ed91dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "# We quantize the inputs using 8-bits\n",
    "concrete_lr = ConcreteLinearRegression(n_bits=8)\n",
    "\n",
    "# We train the concrete linear regression model on clear data\n",
    "concrete_lr.fit(X_train, y_train)\n",
    "\n",
    "# We densify the space representation of the original X,\n",
    "# to better visualize the resulting step function in the following figure\n",
    "x_space = np.linspace(X_test.min(), X_test.max(), num=300)\n",
    "x_space = x_space[:, np.newaxis]\n",
    "y_pred_q_space = concrete_lr.predict(x_space)\n",
    "\n",
    "# Now, we can test our Concrete ML model on the clear test data\n",
    "y_pred_q = concrete_lr.predict(X_test)\n",
    "\n",
    "# Compute the R2 scores\n",
    "quantized_r2_score = r2_score(y_test, y_pred_q)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95815f1a",
   "metadata": {},
   "source": [
    "Now, let's visualize our predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3d953255",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.ioff()\n",
    "\n",
    "plt.clf()\n",
    "fig, ax = plt.subplots(1, figsize=(12, 8))\n",
    "fig.patch.set_facecolor(\"white\")\n",
    "ax.scatter(X_train, y_train, **train_plot_config)\n",
    "ax.scatter(X_test, y_test, **test_plot_config)\n",
    "ax.plot(X_test, y_pred, **get_sklearn_plot_config(sklearn_r2_score))\n",
    "ax.plot(x_space, y_pred_q_space, **get_concrete_plot_config(quantized_r2_score))\n",
    "ax.legend()\n",
    "display(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6808065",
   "metadata": {},
   "source": [
    "As you can see, the quantized model almost perfectly matches its float equivalent model inside the training domain.\n",
    "There is however a very small decrease in the performance as the model poorly generalizes outside of it."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd74c5e7",
   "metadata": {},
   "source": [
    "### 2.2 Quantized Linear Regression with FHE\n",
    "\n",
    "\n",
    "To perform homomorphic inference, we take the above trained quantized model and we compile it to get an FHE model.\n",
    " \n",
    "The compiler requires an exhaustive set of data to evaluate the maximum integer bit-width within the graph, which is needed during the FHE computations before running any predictions. \n",
    "\n",
    "The user can either provide the entire train data-set or a smaller but representative subset of it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b8f8f95b",
   "metadata": {},
   "outputs": [],
   "source": [
    "fhe_circuit = concrete_lr.compile(X_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f58f1b8b",
   "metadata": {},
   "source": [
    "#### Generate the key\n",
    "\n",
    "The compiler returns a circuit, which can then be used for key generation and predictions. More precisely, it generates:\n",
    "- a Secret Key, used for the encryption and decryption processes. This key should remain accessible only to the user.\n",
    "- an Evaluation Key, used to evaluate the circuit on encrypted data. Anyone could access this key without breaching the model's security."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8fd94d07",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generating a key for a 9-bit circuit\n"
     ]
    }
   ],
   "source": [
    "print(f\"Generating a key for a {fhe_circuit.graph.maximum_integer_bit_width()}-bit circuit\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "afced67d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Key generation time: 0.0002 seconds\n"
     ]
    }
   ],
   "source": [
    "time_begin = time.time()\n",
    "fhe_circuit.client.keygen(force=False)\n",
    "print(f\"Key generation time: {time.time() - time_begin:.4f} seconds\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f28155cf",
   "metadata": {},
   "source": [
    "Now that the model has been compiled, inference can be performed on encrypted data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2b6da1f6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Execution time: 0.0033 seconds per sample\n"
     ]
    }
   ],
   "source": [
    "time_begin = time.time()\n",
    "y_pred_fhe = concrete_lr.predict(X_test, fhe=\"execute\")\n",
    "print(f\"Execution time: {(time.time() - time_begin) / len(X_test):.4f} seconds per sample\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23852861",
   "metadata": {},
   "source": [
    "### Evaluate all the models\n",
    "\n",
    "In the following, we use $R^2$-score metric to evaluate each model's performance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "33c4560e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 scores:\n",
      "scikit-learn (clear): 0.9013\n",
      "Concrete ML (quantized): 0.8973\n",
      "Concrete ML (FHE): 0.8973\n",
      "\n",
      "Relative score difference for Concrete ML (quantized clear) vs. Concrete ML (FHE): 0.00%\n",
      "Relative score difference for scikit-learn (clear) vs. Concrete ML (FHE) scores: 0.45%\n"
     ]
    }
   ],
   "source": [
    "# Measure the FHE R2 score\n",
    "fhe_r2_score = r2_score(y_test, y_pred_fhe)\n",
    "\n",
    "print(\"R^2 scores:\")\n",
    "print(f\"scikit-learn (clear): {sklearn_r2_score:.4f}\")\n",
    "print(f\"Concrete ML (quantized): {quantized_r2_score:.4f}\")\n",
    "print(f\"Concrete ML (FHE): {fhe_r2_score:.4f}\")\n",
    "\n",
    "# Measure the error of the FHE quantized model with respect to the clear scikit-learn float model\n",
    "concrete_score_difference = abs(fhe_r2_score - quantized_r2_score) * 100 / quantized_r2_score\n",
    "print(\n",
    "    \"\\nRelative score difference for Concrete ML (quantized clear) vs. Concrete ML (FHE):\",\n",
    "    f\"{concrete_score_difference:.2f}%\",\n",
    ")\n",
    "\n",
    "# Measure the error of the FHE quantized model with respect to the clear float model\n",
    "score_difference = abs(fhe_r2_score - sklearn_r2_score) * 100 / sklearn_r2_score\n",
    "print(\n",
    "    \"Relative score difference for scikit-learn (clear) vs. Concrete ML (FHE) scores:\",\n",
    "    f\"{score_difference:.2f}%\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c228713f",
   "metadata": {},
   "source": [
    "We can observe that scikit-learn and Concrete ML models output very close $R^2$ scores. This demonstrate how the quantization process has a very limited impact on performances. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "704b2f63",
   "metadata": {},
   "source": [
    "### Plot the results of the Sklearn model and the FHE one"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c8f99bc3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# For better visualization\n",
    "y_pred_q_space = concrete_lr.predict(x_space)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "aae3f6da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.clf()\n",
    "fig, ax = plt.subplots(1, figsize=(12, 8))\n",
    "fig.patch.set_facecolor(\"white\")\n",
    "ax.scatter(X_train, y_train, **train_plot_config)\n",
    "ax.scatter(X_test, y_test, **test_plot_config)\n",
    "ax.plot(X_test, y_pred, **get_sklearn_plot_config(sklearn_r2_score))\n",
    "ax.plot(x_space, y_pred_q_space, **get_concrete_plot_config(fhe_r2_score))\n",
    "ax.legend()\n",
    "\n",
    "display(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a0afd7d",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "In this tutorial, we have shown how easy it is to train and execute a linear regression model in FHE using Concrete ML. \n",
    "\n",
    "We have also discussed the development flow of an FHE model: training, quantization, compilation and inference.\n",
    "\n",
    "The slight decrease in prediction quality is due to the quantization of the model's weights and input data, which makes the model poorly generalize outside of its training domain. However, this decrease remains negligible as both floating point (scikit-learn) and FHE (Concrete ML) models give almost identical R2 scores.\n"
   ]
  }
 ],
 "metadata": {
  "execution": {
   "timeout": 10800
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
